# lohboot

##### Bootstrap Confidence Bands for Summary Function

Computes a bootstrap confidence band for a summary function of a point process.

- Keywords
- spatial, nonparametric

##### Usage

```
lohboot(X,
fun=c("pcf", "Kest", "Lest", "pcfinhom", "Kinhom", "Linhom"),
..., nsim=200, confidence=0.95, global=FALSE, type=7)
```

##### Arguments

- X
- A point pattern (object of class
`"ppp"`

). - fun
- Name of the summary function to be computed: one of the strings
`"pcf"`

,`"Kest"`

,`"Lest"`

,`"pcfinhom"`

,`"Kinhom"`

or`"Linhom"`

. - ...
- Arguments passed to the corresponding local version of the summary function (see Details).
- nsim
- Number of bootstrap simulations.
- confidence
- Confidence level, as a fraction between 0 and 1.
- global
- Logical. If
`FALSE`

(the default), pointwise confidence intervals are constructed. If`TRUE`

, a global (simultaneous) confidence band is constructed. - type
- Integer. Argument passed to
`quantile`

controlling the way the quantiles are calculated.

##### Details

This algorithm computes
confidence bands for the true value of the summary statistic
`fun`

using the bootstrap method of Loh (2008).

If `fun="pcf"`

, for example, the algorithm computes a pointwise
`(100 * confidence)`

% confidence interval for the true value of
the pair correlation function `pcf`

for the point
process. It starts by computing the array of
*local* pair correlation functions,
`localpcf`

, of the data pattern `X`

.
This array consists of the contributions to `pcf`

from each
data point. Then these contributions are resampled `nsim`

times
with replacement; from each resampled dataset the total contribution
is computed, yielding `nsim`

random pair correlation functions.
The pointwise `alpha/2`

and `1 - alpha/2`

quantiles of
these functions are computed, where `alpha = 1 - confidence`

.

To control the smoothing and estimation algorithm, use the
arguments `...`

, which are passed to the local version
of the summary function, as shown below:
**fun** **local version**
`pcf`

`localpcf`

`Kest`

`localK`

`Lest`

`localK`

`pcfinhom`

`localpcfinhom`

`Kinhom`

`localKinhom`

`Linhom`

`localKinhom`

}
For `fun="Lest"`

, the calculations are first performed
as if `fun="Kest"`

, and then the square-root transformation is
applied to obtain the $L$-function.
An alternative to `lohboot`

is `varblock`

.

##### Value

- A function value table
(object of class
`"fv"`

) containing columns giving the estimate of the summary function, the upper and lower limits of the bootstrap confidence interval, and the theoretical value of the summary function for a Poisson process.

##### References

Loh, J.M. (2008)
A valid and fast spatial bootstrap for correlation functions.
*The Astrophysical Journal*, **681**, 726--734.

##### See Also

Summary functions
`Kest`

,
`pcf`

,
`Kinhom`

,
`pcfinhom`

,
`localK`

,
`localpcf`

,
`localKinhom`

,
`localpcfinhom`

.

See `varblock`

for an alternative bootstrap technique.

##### Examples

```
p <- lohboot(simdat, stoyan=0.5)
plot(p)
```

*Documentation reproduced from package spatstat, version 1.37-0, License: GPL (>= 2)*